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A broadband fixed-beam leaky-wave antenna is presented in this thesis. The proposed antenna consists of a graded dielectric superstrate placed on top of a closely-spaced thin slot array. The graded dielectric superstrate is designed using transformation electromagnetics to couple the radiation from underlying leaky slot-line into free space. Wave propagation in graded dielectric media, properties of leaky-wave antennas, and conformal transformation electromagnetics have been explored prior to the design. The behaviour of the proposed antenna has been subsequently improved through developing a technique that exploits transformation electromagnetics. The technique adjusts the discrepancy in phase produced as a result of coordinate stretching at the boundary of transformed medium. Full-wave simulations are carried out to demonstrate the performance of the leaky-wave antenna. Broadband radiation characteristics are achieved from the antenna with peak radiation around 33⁰, 30% side-lobe level, 53% back-lobe level, 30.6⁰ beamwidth, and 11.8 directivity. Such performance makes the antenna suitable for planar applications where a fixed oblique beam is required over a broad bandwidth.